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Vibrations of Nonlocal Polymer-GPL Plates at Nanoscale: Application of a Quasi-3D Plate Model

Author

Listed:
  • Yunhe Zou

    (School of Mechanical Engineering, Inner Mongolia University of Technology, Hohhot 010051, China
    Inner Mongolia Key Laboratory of Special Service Intelligent Robotics, Hohhot 010051, China)

  • Yaser Kiani

    (Faculty of Engineering, Shahrekord Univeristy, Shahrekord P.O. Box 115, Iran)

Abstract

An analysis is performed in this research to obtain the natural frequencies of a graphene-platelet-reinforced composite plate at nanoscale. To this end, the nonlocal elasticity theory is applied. A composite laminated plate is considered where each layer is reinforced with GPLs. The amount of GPLs may be different between the layers, which results in functionally graded media. To establish the governing equations of the plate, a quasi-3D plate model is used, which takes the non-uniform shear strains as well as normal strain through the thickness into account. With the aid of the Hamilton principle, the governing equations of the plate are established. For the case of a plate that is simply supported all around, natural frequencies are obtained using the well-known Navier solution method. The results of this study are compared with the available data in the open literature, and, after that, novel numerical results are provided to explore the effects of different parameters. It is depicted that, with the introduction of GPLs in the matrix of the composite media, the natural frequencies of the plate enhance. Also, a proper graded pattern in GPL-reinforced composite plates, i.e., an FG-X pattern, results in the maximum frequencies of the plate. In addition, the introduced quasi-3D plate theory is accurate in the estimation of the natural frequencies of thick nanocomposite plates at nanoscale.

Suggested Citation

  • Yunhe Zou & Yaser Kiani, 2023. "Vibrations of Nonlocal Polymer-GPL Plates at Nanoscale: Application of a Quasi-3D Plate Model," Mathematics, MDPI, vol. 11(19), pages 1-18, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4109-:d:1250172
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    References listed on IDEAS

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    1. Ammar Melaibari & Ahmed Amine Daikh & Muhammad Basha & Ahmed Wagih & Ramzi Othman & Khalid H. Almitani & Mostafa A. Hamed & Alaa Abdelrahman & Mohamed A. Eltaher, 2022. "A Dynamic Analysis of Randomly Oriented Functionally Graded Carbon Nanotubes/Fiber-Reinforced Composite Laminated Shells with Different Geometries," Mathematics, MDPI, vol. 10(3), pages 1-24, January.
    2. Farzad Ebrahimi & Hosein Ezzati, 2023. "A Machine-Learning-Based Model for Buckling Analysis of Thermally Affected Covalently Functionalized Graphene/Epoxy Nanocomposite Beams," Mathematics, MDPI, vol. 11(6), pages 1-13, March.
    3. Mahmure Avey & Nicholas Fantuzzi & Abdullah Sofiyev, 2022. "Mathematical Modeling and Analytical Solution of Thermoelastic Stability Problem of Functionally Graded Nanocomposite Cylinders within Different Theories," Mathematics, MDPI, vol. 10(7), pages 1-11, March.
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